Equation 22 · Patterning at the Limit: What Actually Happens When a Chip Is Manufactured
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the cluster parameter [ 16 ]. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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The Poisson limit exposes the die-area relationship in one line. Because the exponent is linear in area, doubling die area squares the yield: Y(2S) = Y(S)^2 . A part yielding 80 per cent at one size yields 64 per cent at twice the size and about 41 per cent at four times. Yield does not decline with area; it decays geometrically. Finite c softens this — real defects cluster, clustered defects waste fewer dies than scattered ones, and this is precisely why the industry prefers the negative binomial form over Poisson, which systematically understates large-die yield.
Sources cited in the article section
- [2] International Roadmap for Devices and Systems 2023 Update: Yield Enhancement ↗
- [16] Chiplet Actuary: A Quantitative Cost Model and Multi-Chiplet Architecture Exploration ↗
- [1] International Roadmap for Devices and Systems 2023 Update: Lithography and Patterning ↗
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